[formalsystem]

This is a great book but a bit dense first. At a high level it goes through physics with an optimization viewpoint, as in find the actions that minimize a system's energy to figure out how a system will evolve.

I would strongly suggest you learn Lagrangian and Hamiltonian Mechanics from this book first [1] since it comes with many more illustrations and simple arguments that'll make reading SICM much easier. If you don't have time to read a whole book and want to get the main idea I've written a blog post about Lagragian mechanics myself [2] which has made it to the front page of Hacker News before. The great thing about SICM is that it's a physics textbook where the formulas are replaced by code [3] which you means you can play around with your assumptions to gain intuition for how everything works.

IMO I believe in introductory physics we overemphasize formalism over intuition and playing around with simulators is a truer way to explore physics since most physical laws were derived via experimentation not derivation. Another book that really drives this point home is [4]

[1] https://www.amazon.com/Jakob-Schwichtenberg/dp/1096195380/re...

[2] https://blog.usejournal.com/how-to-turn-physics-into-an-opti...

[3] https://github.com/hnarayanan/sicm

[4] https://natureofcode.com/

[petermcneeley]

"find the actions that minimize a system's energy" That sounds incorrect.

The path taken by the system between times t1 and t2 and configurations q1 and q2 is the one for which the action is stationary (no change) to first order. https://en.wikipedia.org/wiki/Principle_of_least_action

The reason for this is quantum mechanics https://en.wikipedia.org/wiki/Path_integral_formulation

[formalsystem]

Yes you're correct, I'm just giving the intuition that I found helpful to understand the Principle of Least Action.

[cambalache]

> The reason for this is quantum mechanics https://en.wikipedia.org/wiki/Path_integral_formulation

This is incorrect. You dont need QM to formulate, derive or use the LAP. This makes even less sense in the context of the book.

[petermcneeley]

"Its classical mechanics and electromagnetic expressions are a consequence of quantum mechanics, but the stationary action method helped in the development of quantum mechanics."

[cambalache]

That is a direct quote from the article in Wikipedia which refers to Feynman's popular book "The character of the physical law". In that book Feynman DID NOT claim that the theory of Quantum Mechanics implies the PLA for classical mechanics, relativity or EM. The closest statement Feynman wrote in that book is this: "In fact it turns out that in quantum mechanics neither is right in exactly the way I have stated them, but the fact that a minimum principle exists turns out to be a consequence of the fact that on a small scale particles obey quantum mechanics." This is a very different statement and it shows a misunderstanding from the Wikipedia editor (and it seems you too). Here Feynman explicitly claims that the fact that there is a PLA in QM is a consequence of small particles obeying QM , that is , they are equivalent.Same way as the fact that particles obey Newton's Laws imply the existence of a principle of least action in classical mechanics, as formulated originally by Lagrange.

[petermcneeley]

This has nothing to do with Feynman. The deep mystery is always why does nature work the way it does. The QM phase answer provides a deep explanation for why least action occurs at a classical level. I am not sure what your educational background is but QM and Classical are far from equivalent. QM looks like classical under many macro situations.

[cambalache]

The quote you wrote exclusively referenced a Feynman book (I suggest you to check your sources), so it was you who brought up Feynman.

> The QM phase answer provides a deep explanation for why least action occurs at a classical level.

No, it does not. The phase in a QM state provides the intereference of the probabilities, which is an integral part in the calculations on the many-paths formulation of QM, it has NOTHING to do in the classical sense.If that is true, please derive the GR action from QM, if you do so a Nobel prize and a seat along Newton and Einstein are waiting for you.

> QM and Classical are far from equivalent. QM looks like classical under many macro situations.

These two statements are contradictory.Maybe you are misremembering the Ehrenfest theorem. If that is the case you are confusing the expectation value of a physical quantity in QM with an actual physical measurement.

[iana_mania_c]

Great intro. Your link #2 leads into the rabbit-hole CS treatment of classical physics (via automatic differentiation, and, less obviously, type theory). Here's that HN thread accompanying your blog post from 6 months ago

https://news.ycombinator.com/item?id=21460106

On the matter of automatic differentiation, if you check out the scmutils source code, there's been an ongoing effort spanning ~a decade to fix a very subtle bug...

[CamperBob2]

Is there a way to get a better preview of Schwichtenberg's book than what Amazon offers? "Surprise Me" is completely useless these days, it just alternates between the first and last few pages.

[formalsystem]

He has a pretty good blog you can check out http://jakobschwichtenberg.com/

But honestly the book is very cheap relative to how good it is IMO

[seesawtron]

[2] is pretty cool article. It might be the first time I have understood optimization from a mechanics perspective correctly. Thanks for sharing. PS: there are still some errors in the blog I found (Theta, M (not m) in moving cart figure)

[formalsystem]

Thank you, that means a lot - you are right there are still some small errors that I need to go through and I'd be very grateful if you let me know of any more you find